Ratio and Unitary Method Worksheet for Olympiad

Maths Olympiad topic 13: Ratio and the unitary method · Set 180 · 40 questions

How to solve it (Go through one): Unitary: cost of one = total ÷ number; then multiply by how many you need. Ratio p : q of a total: one part = total ÷ (p + q); a share = its parts × one part. Workers and days go the opposite way: total work = workers × days; days = total work ÷ new number of workers.

1. 1.3 workers can build a wall in 12 days. How many days will 6 workers take, working at the same speed? (a) 24 days (b) 15 days (c) 6 days (d) 9 days
2. 2.If 5 notebooks cost ₹40, how much do 10 notebooks cost? (a) ₹80 (b) ₹45 (c) ₹88 (d) ₹400
3. 3.3 workers can build a wall in 7 days. How many days will 7 workers take, working at the same speed? (a) 11 days (b) 4 days (c) 3 days (d) 2 days
4. 4.If 7 notebooks cost ₹28, how much do 8 notebooks cost? (a) ₹32 (b) ₹36 (c) ₹29 (d) ₹224
5. 5.If 9 kites cost ₹99, how much do 3 kites cost? (a) ₹33 (b) ₹44 (c) ₹297 (d) ₹93
6. 6.₹112 is shared between two friends in the ratio 1 : 7. How much is the bigger share? (a) ₹112 (b) ₹98 (c) ₹14 (d) ₹56
7. 7.6 workers can build a wall in 12 days. How many days will 3 workers take, working at the same speed? (a) 24 days (b) 9 days (c) 15 days (d) 6 days
8. 8.If 7 pens cost ₹70, how much do 5 pens cost? (a) ₹60 (b) ₹50 (c) ₹350 (d) ₹68
9. 9.₹264 is shared between two friends in the ratio 3 : 8. How much is the bigger share? (a) ₹24 (b) ₹72 (c) ₹192 (d) ₹132
10. 10.₹35 is shared between two friends in the ratio 1 : 6. How much is the bigger share? (a) ₹35 (b) ₹31 (c) ₹30 (d) ₹5
11. 11.7 workers can build a wall in 14 days. How many days will 2 workers take, working at the same speed? (a) 9 days (b) 4 days (c) 49 days (d) 19 days
12. 12.6 workers can build a wall in 5 days. How many days will 3 workers take, working at the same speed? (a) 2 days (b) 11 days (c) 10 days (d) 8 days
13. 13.If 7 kites cost ₹161, how much do 8 kites cost? (a) ₹162 (b) ₹1288 (c) ₹207 (d) ₹184
14. 14.4 workers can build a wall in 6 days. How many days will 2 workers take, working at the same speed? (a) 4 days (b) 3 days (c) 12 days (d) 8 days
15. 15.3 workers can build a wall in 15 days. How many days will 9 workers take, working at the same speed? (a) 5 days (b) 21 days (c) 9 days (d) 45 days
16. 16.3 workers can build a wall in 4 days. How many days will 12 workers take, working at the same speed? (a) 2 days (b) 16 days (c) 13 days (d) 1 day
17. 17.₹390 is shared between two friends in the ratio 1 : 9. How much is the bigger share? (a) ₹351 (b) ₹390 (c) ₹39 (d) ₹195
18. 18.If 9 notebooks cost ₹99, how much do 11 notebooks cost? (a) ₹1089 (b) ₹132 (c) ₹121 (d) ₹101
19. 19.If 9 pens cost ₹153, how much do 4 pens cost? (a) ₹148 (b) ₹68 (c) ₹612 (d) ₹85
20. 20.If 3 pens cost ₹63, how much do 4 pens cost? (a) ₹105 (b) ₹84 (c) ₹252 (d) ₹64
21. 21.6 workers can build a wall in 5 days. How many days will 2 workers take, working at the same speed? (a) 15 days (b) 9 days (c) 16 days (d) 1 day
22. 22.If 4 mangoes cost ₹44, how much do 2 mangoes cost? (a) ₹42 (b) ₹22 (c) ₹88 (d) ₹33
23. 23.If 4 notebooks cost ₹20, how much do 10 notebooks cost? (a) ₹55 (b) ₹200 (c) ₹26 (d) ₹50
24. 24.If 9 pens cost ₹54, how much do 2 pens cost? (a) ₹12 (b) ₹18 (c) ₹47 (d) ₹108
25. 25.7 workers can build a wall in 5 days. How many days will 5 workers take, working at the same speed? (a) 8 days (b) 7 days (c) 6 days (d) 3 days
26. 26.If 3 pens cost ₹30, how much do 2 pens cost? (a) ₹60 (b) ₹29 (c) ₹30 (d) ₹20
27. 27.8 workers can build a wall in 10 days. How many days will 10 workers take, working at the same speed? (a) 9 days (b) 7 days (c) 8 days (d) 12 days
28. 28.If 5 notebooks cost ₹75, how much do 6 notebooks cost? (a) ₹90 (b) ₹450 (c) ₹76 (d) ₹105
29. 29.If 2 mangoes cost ₹16, how much do 3 mangoes cost? (a) ₹48 (b) ₹17 (c) ₹32 (d) ₹24
30. 30.₹132 is shared between two friends in the ratio 5 : 7. How much is the bigger share? (a) ₹11 (b) ₹77 (c) ₹66 (d) ₹55
31. 31.If 7 pens cost ₹168, how much do 8 pens cost? (a) ₹1344 (b) ₹169 (c) ₹216 (d) ₹192
32. 32.If 6 pens cost ₹126, how much do 3 pens cost? (a) ₹63 (b) ₹84 (c) ₹123 (d) ₹378
33. 33.If 8 notebooks cost ₹32, how much do 9 notebooks cost? (a) ₹36 (b) ₹288 (c) ₹33 (d) ₹40
34. 34.If 7 kites cost ₹28, how much do 11 kites cost? (a) ₹48 (b) ₹32 (c) ₹44 (d) ₹308
35. 35.9 workers can build a wall in 11 days. How many days will 11 workers take, working at the same speed? (a) 10 days (b) 8 days (c) 9 days (d) 13 days
36. 36.If 4 pens cost ₹72, how much do 3 pens cost? (a) ₹72 (b) ₹54 (c) ₹71 (d) ₹216
37. 37.If 8 pens cost ₹176, how much do 4 pens cost? (a) ₹172 (b) ₹110 (c) ₹88 (d) ₹704
38. 38.If 7 kites cost ₹56, how much do 6 kites cost? (a) ₹48 (b) ₹55 (c) ₹56 (d) ₹336
39. 39.4 workers can build a wall in 9 days. How many days will 6 workers take, working at the same speed? (a) 5 days (b) 11 days (c) 6 days (d) 7 days
40. 40.₹70 is shared between two friends in the ratio 5 : 9. How much is the bigger share? (a) ₹35 (b) ₹5 (c) ₹45 (d) ₹25

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